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MULTIPLE CHOICE QUESTIONS ON DEFINITE INTEGRALS

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MULTIPLE CHOICE QUESTIONS ON DEFINITE INTEGRALS
1. Evaluate ∫ ¹ x² dx₀
a) 1/2 b) 1/3 c) 1/4 d) 1/6
Answer: b) 1/3
2. Calculate ∫ π sin(x) dx₀
a) 0 b) 1 c) 2 d) π
Answer: c) 2
3. Find ∫ ² ln(x) dx₁
a) 2ln(2) - 1 b) ln(2) c) 2 - ln(2) d) 1 - ln(2)
Answer: a) 2ln(2) - 1
4. Compute ∫ ¹ e^x dx₀
a) e - 1 b) 1 c) e d) ln(e)
Answer: a) e - 1
5. Evaluate ∫ ² (x³ + 2x) dx₀
a) 8 b) 10 c) 12 d) 14
Answer: b) 10
6. Calculate ∫ π/2 cos²(x) dx₀
a) π/4 b) 1 c) π/2 d) 0
Answer: a) π/4
7. Find ∫ ¹ √(1-x²) dx₀
a) π/4 b) π/2 c) 1 d) 2
Answer: a) π/4
8. Compute ∫ ¹ (1/x) dx₀
a) 0 b) 1 c) ln(2) d) undefined
Answer: d) undefined
9. Evaluate ∫ ² (1/x²) dx₁
a) 1/2 b) -1/2 c) 1 d) -1
Answer: b) -1/2
10. Calculate ∫ π/2 tan(x) dx₀
a) ln(2) b) 1 c) π/2 d) ln(cos(π/2))
Answer: a) ln(2)
11. Find ∫ ¹ x³e^x dx₀
a) e - 3 b) e - 2 c) e - 1 d) e
Answer: a) e - 3
12. Compute ∫ ² (x² + 1)³ dx₀
a) 70/3 b) 62/3 c) 58/3 d) 54/3
Answer: b) 62/3
13. Evaluate ∫ π sin²(x) dx₀
a) π/2 b) π c) 2π d) 0
Answer: a) π/2
14. Calculate ∫ ¹ (x + 1/x) dx₀
a) 1 b) 2 c) ln(2) d) 1 + ln(2)
Answer: d) 1 + ln(2)
15. Find ∫ ¹ (1 - x²)³/² dx₀
a) 3π/16 b) π/4 c) 3π/8 d) π/2
Answer: a) 3π/16
16. Compute ∫ ¹ x ln(x) dx₀
a) -1/4 b) 1/4 c) -1/2 d) 1/2
Answer: a) -1/4
17. Evaluate ∫ π/2 sec(x) dx₀
a) ln(2) b) ln(√2) c) ln(√3) d) ln(√5)
Answer: b) ln(√2)
18. Calculate ∫ ¹ arcsin(x) dx₀
a) 1 b) π/4 c) π/2 d) π/4 + √3/4
Answer: b) π/4
19. Find ∫ π/4 tan²(x) dx₀
a) π/4 b) 1/2 c) 1 d) π/4 - 1
Answer: c) 1
20. Compute ∫ ¹ (1 - x⁴)¹/² dx₀
a) π/4 b) π/2 c) 3π/8 d) π/3
Answer: c) 3π/8
21. Evaluate ∫ ¹ x⁴e^(-x²) dx₀
a) 1/4 b) 3/8 c) 1/2 d) 5/8
Answer: b) 3/8
22. Calculate ∫ π/2 sin³(x) dx₀
a) 2/3 b) 3/4 c) 4/3 d) 1
Answer: a) 2/3
23. Find ∫ ¹ (ln(x))² dx₀
a) 1 b) 2 c) 3 d) 4
Answer: b) 2
24. Compute ∫ ¹ x/(1+x²) dx₀
a) π/4 b) ln(2)/2 c) 1/2 d) 1
Answer: b) ln(2)/2
25. Evaluate ∫ π cos(x)sin(x) dx₀
a) 0 b) 1/2 c) 1 d) 2
Answer: a) 0
26. Calculate ∫ ¹ xe^(-x²) dx₀
a) 1/2 b) -1/2 c) 1/4 d) -1/4
Answer: b) -1/2
27. Find ∫ π/2 x sin(x) dx₀
a) 1 b) π/2 c) π/4 d) 1 - π/2
Answer: a) 1
28. Compute ∫ ¹ x²√(1-x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: b) π/8
29. Evaluate ∫ ¹ arctan(x) dx₀
a) π/4 b) 1 c) π/4 - 1/2 d) π/4 + 1/2
Answer: c) π/4 - 1/2
30. Calculate ∫ π/2 sin(x)cos(x) dx₀
a) 1/2 b) 1 c) 3/4 d) 2/3
Answer: a) 1/2
31. Find ∫ ¹ x/(1+x³) dx₀
a) ln(2)/3 b) 1/3 c) π/6 d) √3/3
Answer: b) 1/3
32. Compute ∫ ¹ (1-x²)⁵/² dx₀
a) 8/15 b) 16/35 c) 32/35 d) 64/105
Answer: b) 16/35
33. Evaluate ∫ π/2 sec³(x) dx₀
a) √2 b) √3 c) 2 d) 3
Answer: c) 2
34. Calculate ∫ ¹ x²ln(x) dx₀
a) -1/9 b) 1/9 c) -2/9 d) 2/9
Answer: a) -1/9
35. Find ∫ ¹ x²arcsin(x) dx₀
a) (π-2)/8 b) (π-3)/8 c) (π-4)/8 d) (π-5)/8
Answer: c) (π-4)/8
36. Compute ∫ π/4 sec(x)tan(x) dx₀
a) 1/2 b) 1/√2 c) 1 d) √2
Answer: b) 1/√2
37. Evaluate ∫ ¹ x³/(1+x⁴) dx₀
a) π/8 b) 1/4 c) ln(2)/4 d) 1/2
Answer: a) π/8
38. Calculate ∫ ¹ (1-x)/(1+x) dx₀
a) ln(2) b) 2ln(2) c) 2-ln(4) d) 2-2ln(2)
Answer: c) 2-ln(4)
39. Find ∫ π/2 cos³(x) dx₀
a) 2/3 b) 1 c) 4/3 d) 3/2
Answer: a) 2/3
40. Compute ∫ ¹ x²e^(-x) dx₀
a) 1 b) 2 c) 3 d) 4
Answer: b) 2
41. Evaluate ∫ ¹ √(x³(1-x)) dx₀
a) 3π/16 b) π/5 c) 2π/15 d) π/6
Answer: c) 2π/15
42. Calculate ∫ π/2 ln(sin(x)) dx₀
a) -π/2 b) -π ln(2) c) -π d) -2π
Answer: b) -π ln(2)
43. Find ∫ ¹ (1-x²)⁷/² dx₀
a) 16/35 b) 32/63 c) 64/105 d) 128/315
Answer: c) 64/105
44. Compute ∫ ¹ x arctan(x) dx₀
a) (π-2)/4 b) (π-1)/4 c) π/4 d) (π+1)/4
Answer: b) (π-1)/4
45. Evaluate ∫ π/2 sin(x)ln(cos(x)) dx₀
a) -1 b) 1 c) -2 d) 2
Answer: a) -1
46. Calculate ∫ ¹ x²/(1+x²)² dx₀
a) π/8 b) 1/4 c) π/16 d) 1/8
Answer: b) 1/4
47. Find ∫ ¹ √(1-x⁴) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: b) π/3
48. Compute ∫ ¹ ln(1+x)/x dx₀
a) π²/12 b) π²/6 c) π²/4 d) π²/3
Answer: b) π²/6
49. Evaluate ∫ π/2 tan ¹(sin(x)) dx₀ ⁻
a) π²/16 b) π²/12 c) π²/8 d) π²/6
Answer: c) π²/8
50. Calculate ∫ ¹ x e^(-x²) dx₀ ⁶
a) 5/4 b) 15/8 c) 35/16 d) 63/32
Answer: b) 15/8
51. Find ∫ π/2 sin(x)√(1-sin²(x)) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
52. Compute ∫ ¹ x/(e^x-1) dx₀
a) π²/6 - 1 b) π²/12 - 1/2 c) ζ(2) - 1 d) ζ(3) - 1
Answer: c) ζ(2) - 1
53. Evaluate ∫ ¹ ln(1+x²) dx₀
a) 2 b) π/2 c) 2-π/2 d) π-1
Answer: c) 2-π/2
54. Calculate ∫ π/2 x²sin(x) dx₀
a) π-2 b) π²/4-1 c) π²/2-2 d) π-1
Answer: b) π²/4-1
55. Find ∫ ¹ x²/(1-x²)³/² dx₀
a) 1/2 b) 2/3 c) 3/4 d) 1
Answer: c) 3/4
56. Compute ∫ π/4 ln(tan(x)) dx₀
a) -π ln(2)/4 b) -π ln(2)/2 c) -3π ln(2)/4 d) -π ln(2)
Answer: c) -3π ln(2)/4
57. Evaluate ∫ ¹ x ln(1+x) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
58. Calculate ∫ π/2 x ln(sin(x)) dx₀
a) -π²/8 b) -π²/4 c) -3π²/8 d) -π²/2
Answer: c) -3π²/8
59. Find ∫ ¹ arcsin(x)/√(1-x²) dx₀
a) π/2 b) π c) 3π/2 d) 2π
Answer: b) π
60. Compute ∫ ¹ x³ln(1-x) dx₀
a) -25/32 b) -37/32 c) -49/32 d) -61/32
Answer: c) -49/32
61. Evaluate ∫ π/2 sin(x)ln(1+cos(x)) dx₀
a) ln(2)-1/2 b) ln(2) c) 2ln(2)-1 d) 2ln(2)
Answer: c) 2ln(2)-1
62. Calculate ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
63. Find ∫ ¹ √(x-x²) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: b) π/6
64. Compute ∫ ¹ (arcsin(x))² dx₀
a) π²/8 b) π²/6 c) π²/4 d) π²/3
Answer: b) π²/6
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/365. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
65. Evaluate ∫ ¹ x²√(1-x) dx₀
a) 8/105 b) 16/105 c) 32/105 d) 64/105
Answer: b) 16/105
66. Calculate ∫ π/2 ln(1+tan(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
67. Find ∫ ¹ x³√(1-x²) dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
68. Compute ∫ ¹ x²/(e^x+1) dx₀
a) 1/2 b) 2/3 c) 3/4 d) 5/6
Answer: c) 3/4
69. Evaluate ∫ π/2 sin(x)cos²(x) dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
70. Calculate ∫ ¹ x arcsin(x²) dx₀
a) π/16 b) π/8 c) 3π/16 d) π/4
Answer: c) 3π/16
71. Find ∫ ¹ ln(x+√(1+x²)) dx₀
a) 1 b) √2 c) 3/2 d) 2
Answer: a) 1
72. Compute ∫ π/2 sec⁴(x) dx₀
a) 1/3 b) 2/3 c) 1 d) 4/3
Answer: b) 2/3
73. Evaluate ∫ ¹ x⁴ln(x) dx₀
a) -1/25 b) -1/50 c) -1/100 d) -1/125
Answer: a) -1/25
74. Calculate ∫ π/4 csc²(x) dx₀
a) 1 b) √2 c) 2 d) 3
Answer: a) 1
75. Find ∫ ¹ x²/(1+x⁴) dx₀
a) π/8 b) π/6 c) π/4 d) π/3
Answer: a) π/8
76. Compute ∫ π/2 sin(x)cos(3x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
77. Evaluate ∫ ¹ (1-x²) /² dx₀ ⁹
a) 128/315 b) 256/315 c) 512/315 d) 1024/315
Answer: b) 256/315
78. Calculate ∫ ¹ x³arccos(x) dx₀
a) π/16 b) π/12 c) π/8 d) π/6
Answer: c) π/8
79. Find ∫ ¹ x ln²(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
80. Compute ∫ π/2 ln(cos(x)) dx₀
a) -π ln(2)/2 b) -π ln(2) c) -3π ln(2)/2 d) -2π ln(2)
Answer: a) -π ln(2)/2
81. Evaluate ∫ ¹ x²e^(-x²) dx₀
a) (√π/4)(1-e ¹) b) (√π/4)(1-2e ¹) c) (√π/4)(1-3e ¹) d) (√π/4)(1-4e ¹)⁻ ⁻ ⁻ ⁻
Answer: a) (√π/4)(1-e ¹)⁻
82. Calculate ∫ π/2 tan³(x) dx₀
a) π/4 b) π/3 c) π/2 d) 2π/3
Answer: c) π/2
83. Find ∫ ¹ x⁵√(1-x²) dx₀
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
84. Compute ∫ ¹ (ln(x))³ dx₀
a) -3/2 b) -5/2 c) -7/2 d) -9/2
Answer: c) -7/2
85. Evaluate ∫ π/2 sin(x)ln(1+sin(x)) dx₀
a) π/2 b) 2-ln(4) c) π/2-ln(2) d) 2-π/2
Answer: b) 2-ln(4)
86. Calculate ∫ ¹ x³/(1-x²)⁵/² dx₀
a) 1/6 b) 1/3 c) 1/2 d) 2/3
Answer: b) 1/3
87. Find ∫ π/4 sec⁵(x) dx₀
a) 1/4 b) 1/3 c) 1/2 d) 2/3
Answer: c) 1/2
88. Compute ∫ ¹ x²arctan(x) dx₀
a) (π-2)/12 b) (π-1)/6 c) π/4 d) (π+2)/12
Answer: b) (π-1)/6
89. Evaluate ∫ ¹ √(x³/(1-x)) dx₀
a) π/3 b) 2π/3 c) π d) 4π/3
Answer: c) π
Answer: c) π
90. Calculate ∫ π/2 cos(x)ln(sin(x)) dx₀
a) -1 b) -2 c) -3 d) -4
Answer: a) -1
91. Find ∫ ¹ x⁴/(1+x²)³ dx₀
a) 1/8 b) 3/16 c) 1/4 d) 5/16
Answer: b) 3/16
92. Compute ∫ π/2 sin²(x)cos²(x) dx₀
a) 1/8 b) 1/6 c) 1/4 d) 1/3
Answer: a) 1/8
93. Evaluate ∫ ¹ x²ln²(x) dx₀
a) 2/9 b) 4/9 c) 2/3 d) 8/9
Answer: b) 4/9
94. Calculate ∫ π/4 ln(tan(x)) dx₀
a) -G b) -2G c) -3G d) -4G
Answer: a) -G (where G is Catalan's constant)
95. Find ∫ ¹ x arcsin²(x) dx₀
a) (π²-4)/24 b) (π²-4)/16 c) (π²-4)/12 d) (π²-4)/8
Answer: c) (π²-4)/12
96. Compute ∫ ¹ x √(1-x²) dx₀ ⁶
a) 5π/128 b) 5π/64 c) 5π/32 d) 5π/16
Answer: b) 5π/64
97. Evaluate ∫ π/2 sin(x)cos(x)ln(sin(x)) dx₀
a) -1/4 b) -1/3 c) -1/2 d) -2/3
Answer: c) -1/2
98. Calculate ∫ ¹ x³ln(1+x²) dx₀
a) 11/36 b) 13/36 c) 15/36 d) 17/36
Answer: b) 13/36
99. Find ∫ ¹ x²/(e^x-1) dx₀
a) ζ(3)-1 b) ζ(3)-2 c) 2ζ(3)-1 d) 2ζ(3)-2
Answer: a) ζ(3)-1 (where ζ is the Riemann zeta function)
100. Compute ∫ π/2 ln(1+sin²(x)) dx₀
a) π ln(2)/2 b) π ln(2) c) 3π ln(2)/2 d) 2π ln(2)
Answer: b) π ln(2)
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